df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))
index = sample(1:nrow(df), 0.7*nrow(df))
train = df[index,] # Create the training data
test = df[-index,] # Create the test data
dim(train)
## [1] 1119 12
dim(test)
## [1] 480 12
lm_basic <- lm(data = df, quality ~ .)
summary(lm_basic)
##
## Call:
## lm(formula = quality ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16
Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.
train_control <- trainControl(method = "cv", number = 5)
model_ridge <- train(quality ~ .,
data = df,
method = "ridge", # method
trControl = train_control) # cross validation
model_ridge
## Ridge Regression
##
## 1599 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 1281, 1280, 1279, 1278, 1278
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 0.6506816 0.3540442 0.5043230
## 1e-04 0.6506802 0.3540472 0.5043209
## 1e-01 0.6504990 0.3548844 0.5033013
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.
#something doesn't seem to be working here
model_stepwise <- train(quality ~ .,
data = df,
method = "glmStepAIC",
trControl = train_control)
## Start: AIC=2569.31
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 547.09 2567.5
## - density 1 547.15 2567.6
## - fixed.acidity 1 547.20 2567.7
## - citric.acid 1 547.72 2569.0
## <none> 547.01 2569.3
## - free.sulfur.dioxide 1 548.19 2570.1
## - pH 1 549.84 2573.9
## - total.sulfur.dioxide 1 553.62 2582.7
## - chlorides 1 553.94 2583.4
## - sulphates 1 565.29 2609.3
## - volatile.acidity 1 574.97 2631.1
## - alcohol 1 584.22 2651.5
##
## Step: AIC=2567.49
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + density + pH +
## sulphates + alcohol
##
## Df Deviance AIC
## - density 1 547.15 2565.6
## - fixed.acidity 1 547.21 2565.8
## - citric.acid 1 547.79 2567.1
## <none> 547.09 2567.5
## - free.sulfur.dioxide 1 548.33 2568.4
## - pH 1 550.52 2573.5
## - total.sulfur.dioxide 1 553.64 2580.7
## - chlorides 1 554.03 2581.6
## - sulphates 1 565.51 2607.8
## - volatile.acidity 1 575.06 2629.3
## - alcohol 1 599.28 2682.0
##
## Step: AIC=2565.64
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 547.21 2563.8
## - citric.acid 1 547.87 2565.3
## <none> 547.15 2565.6
## - free.sulfur.dioxide 1 548.41 2566.6
## - pH 1 552.41 2575.9
## - total.sulfur.dioxide 1 554.01 2579.6
## - chlorides 1 554.30 2580.2
## - sulphates 1 565.85 2606.6
## - volatile.acidity 1 576.26 2629.9
## - alcohol 1 639.98 2764.1
##
## Step: AIC=2563.77
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 547.96 2563.5
## <none> 547.21 2563.8
## - free.sulfur.dioxide 1 548.50 2564.8
## - total.sulfur.dioxide 1 555.00 2579.9
## - chlorides 1 555.28 2580.5
## - pH 1 555.47 2580.9
## - sulphates 1 566.06 2605.1
## - volatile.acidity 1 577.87 2631.5
## - alcohol 1 640.60 2763.3
##
## Step: AIC=2563.52
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 547.96 2563.5
## - free.sulfur.dioxide 1 549.56 2565.3
## - pH 1 555.83 2579.8
## - total.sulfur.dioxide 1 556.73 2581.8
## - chlorides 1 557.02 2582.5
## - sulphates 1 566.40 2603.9
## - volatile.acidity 1 582.31 2639.3
## - alcohol 1 641.95 2764.0
## Start: AIC=2560.19
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 542.71 2558.2
## - density 1 542.72 2558.2
## - citric.acid 1 542.73 2558.2
## - residual.sugar 1 542.73 2558.2
## <none> 542.71 2560.2
## - free.sulfur.dioxide 1 544.78 2563.1
## - pH 1 545.45 2564.6
## - total.sulfur.dioxide 1 551.59 2579.0
## - chlorides 1 554.08 2584.7
## - sulphates 1 563.03 2605.2
## - volatile.acidity 1 570.15 2621.3
## - alcohol 1 581.41 2646.3
##
## Step: AIC=2558.2
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 542.73 2556.2
## - citric.acid 1 542.73 2556.2
## - residual.sugar 1 542.74 2556.3
## <none> 542.71 2558.2
## - free.sulfur.dioxide 1 544.79 2561.1
## - pH 1 548.08 2568.8
## - total.sulfur.dioxide 1 552.05 2578.0
## - chlorides 1 554.64 2584.0
## - sulphates 1 563.53 2604.4
## - volatile.acidity 1 570.25 2619.6
## - alcohol 1 596.88 2678.0
##
## Step: AIC=2556.23
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 542.74 2554.3
## - residual.sugar 1 542.78 2554.4
## <none> 542.73 2556.2
## - free.sulfur.dioxide 1 544.81 2559.1
## - pH 1 548.08 2566.8
## - total.sulfur.dioxide 1 552.36 2576.8
## - chlorides 1 554.93 2582.7
## - sulphates 1 564.71 2605.1
## - volatile.acidity 1 572.07 2621.6
## - alcohol 1 629.63 2744.3
##
## Step: AIC=2554.26
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 542.79 2552.4
## <none> 542.74 2554.3
## - free.sulfur.dioxide 1 544.92 2557.4
## - pH 1 549.19 2567.4
## - total.sulfur.dioxide 1 552.66 2575.4
## - chlorides 1 555.26 2581.4
## - sulphates 1 564.85 2603.4
## - volatile.acidity 1 580.85 2639.1
## - alcohol 1 632.02 2747.2
##
## Step: AIC=2552.37
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 542.79 2552.4
## - free.sulfur.dioxide 1 545.06 2555.7
## - pH 1 549.40 2565.9
## - total.sulfur.dioxide 1 552.68 2573.5
## - chlorides 1 555.26 2579.4
## - sulphates 1 564.85 2601.4
## - volatile.acidity 1 580.86 2637.1
## - alcohol 1 633.89 2749.0
## Start: AIC=2514.74
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - free.sulfur.dioxide 1 524.58 2513.8
## - pH 1 524.90 2514.5
## <none> 524.16 2514.7
## - density 1 525.05 2514.9
## - residual.sugar 1 525.54 2516.1
## - fixed.acidity 1 525.55 2516.1
## - citric.acid 1 526.83 2519.2
## - chlorides 1 528.06 2522.2
## - total.sulfur.dioxide 1 528.46 2523.2
## - sulphates 1 547.27 2567.9
## - volatile.acidity 1 556.39 2589.0
## - alcohol 1 561.00 2599.6
##
## Step: AIC=2513.75
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - pH 1 525.19 2513.2
## <none> 524.58 2513.8
## - density 1 525.58 2514.2
## - fixed.acidity 1 526.14 2515.6
## - residual.sugar 1 526.17 2515.6
## - citric.acid 1 527.69 2519.3
## - chlorides 1 528.34 2520.9
## - total.sulfur.dioxide 1 529.35 2523.3
## - sulphates 1 548.25 2568.2
## - volatile.acidity 1 558.92 2592.8
## - alcohol 1 561.30 2598.3
##
## Step: AIC=2513.24
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + sulphates +
## alcohol
##
## Df Deviance AIC
## <none> 525.19 2513.2
## - residual.sugar 1 527.76 2517.5
## - citric.acid 1 528.10 2518.3
## - density 1 528.28 2518.8
## - chlorides 1 528.48 2519.2
## - total.sulfur.dioxide 1 529.58 2521.9
## - fixed.acidity 1 531.86 2527.4
## - sulphates 1 549.97 2570.2
## - volatile.acidity 1 559.48 2592.1
## - alcohol 1 568.64 2612.9
## Start: AIC=2510.97
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 522.65 2509.0
## - density 1 523.03 2510.0
## - residual.sugar 1 523.10 2510.1
## - fixed.acidity 1 523.15 2510.3
## - pH 1 523.40 2510.9
## <none> 522.62 2511.0
## - free.sulfur.dioxide 1 525.44 2515.9
## - chlorides 1 526.74 2519.0
## - total.sulfur.dioxide 1 529.60 2525.9
## - volatile.acidity 1 540.25 2551.4
## - sulphates 1 547.99 2569.6
## - alcohol 1 556.17 2588.6
##
## Step: AIC=2509.03
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 523.05 2508.0
## - residual.sugar 1 523.11 2508.2
## - fixed.acidity 1 523.16 2508.3
## - pH 1 523.42 2508.9
## <none> 522.65 2509.0
## - free.sulfur.dioxide 1 525.62 2514.3
## - chlorides 1 527.20 2518.1
## - total.sulfur.dioxide 1 530.38 2525.8
## - volatile.acidity 1 546.62 2564.4
## - sulphates 1 548.00 2567.6
## - alcohol 1 556.47 2587.2
##
## Step: AIC=2508.02
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 523.16 2506.3
## - residual.sugar 1 523.19 2506.4
## <none> 523.05 2508.0
## - pH 1 525.39 2511.7
## - free.sulfur.dioxide 1 526.23 2513.8
## - chlorides 1 527.88 2517.8
## - total.sulfur.dioxide 1 531.02 2525.4
## - sulphates 1 548.44 2566.6
## - volatile.acidity 1 548.92 2567.8
## - alcohol 1 621.88 2727.4
##
## Step: AIC=2506.3
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 523.33 2504.7
## <none> 523.16 2506.3
## - free.sulfur.dioxide 1 526.33 2512.0
## - chlorides 1 528.29 2516.8
## - pH 1 528.44 2517.1
## - total.sulfur.dioxide 1 531.73 2525.1
## - sulphates 1 549.40 2566.9
## - volatile.acidity 1 549.61 2567.4
## - alcohol 1 621.92 2725.4
##
## Step: AIC=2504.71
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 523.33 2504.7
## - free.sulfur.dioxide 1 526.65 2510.8
## - chlorides 1 528.35 2514.9
## - pH 1 528.85 2516.1
## - total.sulfur.dioxide 1 531.73 2523.1
## - sulphates 1 549.40 2564.9
## - volatile.acidity 1 549.76 2565.7
## - alcohol 1 624.71 2729.2
## Start: AIC=2511.04
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 522.89 2509.6
## - fixed.acidity 1 522.89 2509.6
## - residual.sugar 1 523.37 2510.8
## - citric.acid 1 523.43 2511.0
## <none> 522.65 2511.0
## - free.sulfur.dioxide 1 523.56 2511.3
## - pH 1 524.16 2512.7
## - total.sulfur.dioxide 1 529.81 2526.4
## - chlorides 1 530.59 2528.3
## - sulphates 1 543.90 2560.0
## - volatile.acidity 1 552.85 2580.9
## - alcohol 1 559.46 2596.1
##
## Step: AIC=2509.62
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 522.92 2507.7
## - residual.sugar 1 523.37 2508.8
## - citric.acid 1 523.66 2509.5
## <none> 522.89 2509.6
## - free.sulfur.dioxide 1 523.89 2510.1
## - pH 1 526.30 2515.9
## - total.sulfur.dioxide 1 530.34 2525.7
## - chlorides 1 531.21 2527.8
## - sulphates 1 544.30 2559.0
## - volatile.acidity 1 553.99 2581.5
## - alcohol 1 624.48 2734.7
##
## Step: AIC=2507.69
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 523.42 2506.9
## <none> 522.92 2507.7
## - citric.acid 1 523.79 2507.8
## - free.sulfur.dioxide 1 523.95 2508.2
## - pH 1 528.12 2518.4
## - total.sulfur.dioxide 1 531.23 2525.9
## - chlorides 1 532.21 2528.2
## - sulphates 1 544.54 2557.5
## - volatile.acidity 1 555.45 2582.9
## - alcohol 1 625.67 2735.2
##
## Step: AIC=2506.93
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 524.13 2506.7
## <none> 523.42 2506.9
## - free.sulfur.dioxide 1 524.64 2507.9
## - pH 1 528.72 2517.8
## - total.sulfur.dioxide 1 531.48 2524.5
## - chlorides 1 532.56 2527.1
## - sulphates 1 544.69 2555.9
## - volatile.acidity 1 555.53 2581.1
## - alcohol 1 627.55 2737.0
##
## Step: AIC=2506.66
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 524.13 2506.7
## - free.sulfur.dioxide 1 525.66 2508.4
## - pH 1 528.78 2515.9
## - total.sulfur.dioxide 1 533.22 2526.7
## - chlorides 1 534.50 2529.7
## - sulphates 1 545.09 2554.8
## - volatile.acidity 1 560.18 2589.7
## - alcohol 1 628.94 2737.8
## Start: AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 666.70 3163.0
## - fixed.acidity 1 666.80 3163.2
## - residual.sugar 1 666.91 3163.5
## - citric.acid 1 667.06 3163.8
## <none> 666.41 3164.3
## - free.sulfur.dioxide 1 668.10 3166.3
## - pH 1 668.37 3167.0
## - chlorides 1 674.80 3182.3
## - total.sulfur.dioxide 1 674.84 3182.4
## - sulphates 1 693.38 3225.7
## - volatile.acidity 1 700.03 3241.0
## - alcohol 1 712.08 3268.3
##
## Step: AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 666.81 3161.2
## - residual.sugar 1 666.93 3161.5
## - citric.acid 1 667.35 3162.5
## <none> 666.70 3163.0
## - free.sulfur.dioxide 1 668.53 3165.3
## - pH 1 671.02 3171.3
## - total.sulfur.dioxide 1 675.43 3181.8
## - chlorides 1 675.46 3181.8
## - sulphates 1 693.98 3225.1
## - volatile.acidity 1 701.70 3242.8
## - alcohol 1 786.37 3424.9
##
## Step: AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 667.06 3159.8
## - citric.acid 1 667.37 3160.6
## <none> 666.81 3161.2
## - free.sulfur.dioxide 1 668.71 3163.8
## - pH 1 673.87 3176.1
## - chlorides 1 676.75 3182.9
## - total.sulfur.dioxide 1 676.84 3183.1
## - sulphates 1 694.48 3224.2
## - volatile.acidity 1 703.04 3243.8
## - alcohol 1 787.44 3425.1
##
## Step: AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 667.54 3159.0
## <none> 667.06 3159.8
## - free.sulfur.dioxide 1 669.13 3162.8
## - pH 1 674.20 3174.9
## - total.sulfur.dioxide 1 676.89 3181.2
## - chlorides 1 676.89 3181.2
## - sulphates 1 694.51 3222.3
## - volatile.acidity 1 703.04 3241.8
## - alcohol 1 789.73 3427.8
##
## Step: AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 667.54 3159.0
## - free.sulfur.dioxide 1 669.93 3162.7
## - pH 1 674.61 3173.8
## - total.sulfur.dioxide 1 678.32 3182.6
## - chlorides 1 678.35 3182.7
## - sulphates 1 694.60 3220.5
## - volatile.acidity 1 709.85 3255.3
## - alcohol 1 792.02 3430.4
#model_stepwise
findCorrelation(
cor(df),
cutoff = 0.5,
verbose = TRUE,
names = TRUE
)
## Compare row 3 and column 1 with corr 0.672
## Means: 0.293 vs 0.19 so flagging column 3
## Compare row 1 and column 8 with corr 0.668
## Means: 0.245 vs 0.172 so flagging column 1
## Compare row 7 and column 6 with corr 0.668
## Means: 0.174 vs 0.169 so flagging column 7
## All correlations <= 0.5
## [1] "citric.acid" "fixed.acidity" "total.sulfur.dioxide"
ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")
df_less_acid <- df %>%
select(-citric.acid, -fixed.acidity)
lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)
##
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.66740 -0.37223 -0.04556 0.46264 2.03092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.0575013 12.0089257 1.004 0.3155
## volatile.acidity -1.0127925 0.1009279 -10.035 < 2e-16 ***
## residual.sugar 0.0115046 0.0134606 0.855 0.3929
## chlorides -2.0490938 0.3992190 -5.133 3.21e-07 ***
## free.sulfur.dioxide 0.0048741 0.0021385 2.279 0.0228 *
## total.sulfur.dioxide -0.0035687 0.0006939 -5.143 3.03e-07 ***
## density -7.5668358 11.8648390 -0.638 0.5237
## pH -0.4919908 0.1210931 -4.063 5.08e-05 ***
## sulphates 0.9024434 0.1129657 7.989 2.60e-15 ***
## alcohol 0.2810022 0.0201992 13.912 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3562
## F-statistic: 99.22 on 9 and 1589 DF, p-value: < 2.2e-16
plot(df)
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
cols = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol')
pre_proc_val <- preProcess(train[,cols], method = c("center", "scale"))
train[,cols] = predict(pre_proc_val, train[,cols])
test[,cols] = predict(pre_proc_val, test[,cols])
summary(train)
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. :-2.0849 Min. :-2.329919 Min. :-1.36303 Min. :-1.16750
## 1st Qu.:-0.6950 1st Qu.:-0.744594 1st Qu.:-0.90785 1st Qu.:-0.46897
## Median :-0.2317 Median :-0.008551 Median :-0.09862 Median :-0.25941
## Mean : 0.0000 Mean : 0.000000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.5212 3rd Qu.: 0.614255 3rd Qu.: 0.81176 3rd Qu.: 0.02001
## Max. : 4.2278 Max. : 5.936415 Max. : 3.69462 Max. : 9.03108
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :-1.53614 Min. :-1.4285 Min. :-1.2448
## 1st Qu.:-0.36667 1st Qu.:-0.7553 1st Qu.:-0.7563
## Median :-0.16504 Median :-0.2744 Median :-0.2678
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.05676 3rd Qu.: 0.4950 3rd Qu.: 0.4955
## Max. :10.54169 Max. : 5.0152 Max. : 7.3955
## density pH sulphates alcohol
## Min. :-3.517805 Min. :-3.66910 Min. :-1.9481 Min. :-1.9002
## 1st Qu.:-0.608370 1st Qu.:-0.66021 1st Qu.:-0.6163 1st Qu.:-0.8625
## Median :-0.003333 Median :-0.02002 Median :-0.2316 Median :-0.2965
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.588550 3rd Qu.: 0.55615 3rd Qu.: 0.3603 3rd Qu.: 0.5840
## Max. : 3.647929 Max. : 4.46130 Max. : 7.9365 Max. : 3.3827
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.624
## 3rd Qu.:6.000
## Max. :8.000
#generic LM
lm_2 <- lm(quality ~ ., data = train)
summary(lm_2)
##
## Call:
## lm(formula = quality ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.2357 -0.3565 -0.0559 0.4114 2.0607
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.62377 0.01904 295.309 < 2e-16 ***
## fixed.acidity 0.08870 0.05479 1.619 0.105768
## volatile.acidity -0.19879 0.02547 -7.805 1.37e-14 ***
## citric.acid -0.03644 0.03361 -1.084 0.278593
## residual.sugar 0.03404 0.02532 1.344 0.179089
## chlorides -0.08550 0.02384 -3.587 0.000349 ***
## free.sulfur.dioxide 0.02978 0.02640 1.128 0.259610
## total.sulfur.dioxide -0.10307 0.02777 -3.711 0.000217 ***
## density -0.04691 0.04896 -0.958 0.338150
## pH -0.02911 0.03574 -0.815 0.415470
## sulphates 0.14075 0.02292 6.141 1.14e-09 ***
## alcohol 0.28610 0.03272 8.744 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.637 on 1107 degrees of freedom
## Multiple R-squared: 0.3642, Adjusted R-squared: 0.3579
## F-statistic: 57.65 on 11 and 1107 DF, p-value: < 2.2e-16
cols_reg = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol', 'quality')
dummies <- dummyVars(quality ~ ., data = df[,cols_reg])
train_dummies = predict(dummies, newdata = train[,cols_reg])
test_dummies = predict(dummies, newdata = test[,cols_reg])
print(dim(train_dummies)); print(dim(test_dummies))
## [1] 1119 11
## [1] 480 11
x = as.matrix(train_dummies)
y_train = train$quality
x_test = as.matrix(test_dummies)
y_test = test$quality
lambdas <- 10^seq(2, -3, by = -.1)
ridge_reg = glmnet(x, y_train, nlambda = 25, alpha = 0, family = 'gaussian', lambda = lambdas)
summary(ridge_reg)
## Length Class Mode
## a0 51 -none- numeric
## beta 561 dgCMatrix S4
## df 51 -none- numeric
## dim 2 -none- numeric
## lambda 51 -none- numeric
## dev.ratio 51 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numeric
cv_ridge <- cv.glmnet(x, y_train, alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda
## [1] 0.03162278
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
SSE <- sum((predicted - true)^2)
SST <- sum((true - mean(true))^2)
R_square <- 1 - SSE / SST
RMSE = sqrt(SSE/nrow(df))
# Model performance metrics
data.frame(
RMSE = RMSE,
Rsquare = R_square
)
}
# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6338504 0.3637537
# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6757041 0.3457975
lambdas <- 10^seq(2, -3, by = -.1)
# Setting alpha = 1 implements lasso regression
lasso_reg <- cv.glmnet(x, y_train, alpha = 1, lambda = lambdas, standardize = TRUE, nfolds = 5)
# Best
lambda_best <- lasso_reg$lambda.min
lambda_best
## [1] 0.01
lasso_model <- glmnet(x, y_train, alpha = 1, lambda = lambda_best, standardize = TRUE)
predictions_train <- predict(lasso_model, s = lambda_best, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6351857 0.3610703
predictions_test <- predict(lasso_model, s = lambda_best, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6775253 0.3422662
# Set training control
train_cont <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
search = "random",
verboseIter = TRUE)
# Train the model
elastic_reg <- train(quality ~ .,
data = train,
method = "glmnet",
preProcess = c("center", "scale"),
tuneLength = 10,
trControl = train_cont)
## + Fold01.Rep1: alpha=0.62989, lambda=0.003636
## - Fold01.Rep1: alpha=0.62989, lambda=0.003636
## + Fold01.Rep1: alpha=0.29776, lambda=2.394057
## - Fold01.Rep1: alpha=0.29776, lambda=2.394057
## + Fold01.Rep1: alpha=0.28799, lambda=0.824474
## - Fold01.Rep1: alpha=0.28799, lambda=0.824474
## + Fold01.Rep1: alpha=0.94218, lambda=2.531489
## - Fold01.Rep1: alpha=0.94218, lambda=2.531489
## + Fold01.Rep1: alpha=0.35679, lambda=1.223740
## - Fold01.Rep1: alpha=0.35679, lambda=1.223740
## + Fold01.Rep1: alpha=0.63956, lambda=3.222801
## - Fold01.Rep1: alpha=0.63956, lambda=3.222801
## + Fold01.Rep1: alpha=0.65727, lambda=0.001635
## - Fold01.Rep1: alpha=0.65727, lambda=0.001635
## + Fold01.Rep1: alpha=0.23136, lambda=0.011723
## - Fold01.Rep1: alpha=0.23136, lambda=0.011723
## + Fold01.Rep1: alpha=0.08606, lambda=0.018838
## - Fold01.Rep1: alpha=0.08606, lambda=0.018838
## + Fold01.Rep1: alpha=0.27970, lambda=0.518103
## - Fold01.Rep1: alpha=0.27970, lambda=0.518103
## + Fold02.Rep1: alpha=0.62989, lambda=0.003636
## - Fold02.Rep1: alpha=0.62989, lambda=0.003636
## + Fold02.Rep1: alpha=0.29776, lambda=2.394057
## - Fold02.Rep1: alpha=0.29776, lambda=2.394057
## + Fold02.Rep1: alpha=0.28799, lambda=0.824474
## - Fold02.Rep1: alpha=0.28799, lambda=0.824474
## + Fold02.Rep1: alpha=0.94218, lambda=2.531489
## - Fold02.Rep1: alpha=0.94218, lambda=2.531489
## + Fold02.Rep1: alpha=0.35679, lambda=1.223740
## - Fold02.Rep1: alpha=0.35679, lambda=1.223740
## + Fold02.Rep1: alpha=0.63956, lambda=3.222801
## - Fold02.Rep1: alpha=0.63956, lambda=3.222801
## + Fold02.Rep1: alpha=0.65727, lambda=0.001635
## - Fold02.Rep1: alpha=0.65727, lambda=0.001635
## + Fold02.Rep1: alpha=0.23136, lambda=0.011723
## - Fold02.Rep1: alpha=0.23136, lambda=0.011723
## + Fold02.Rep1: alpha=0.08606, lambda=0.018838
## - Fold02.Rep1: alpha=0.08606, lambda=0.018838
## + Fold02.Rep1: alpha=0.27970, lambda=0.518103
## - Fold02.Rep1: alpha=0.27970, lambda=0.518103
## + Fold03.Rep1: alpha=0.62989, lambda=0.003636
## - Fold03.Rep1: alpha=0.62989, lambda=0.003636
## + Fold03.Rep1: alpha=0.29776, lambda=2.394057
## - Fold03.Rep1: alpha=0.29776, lambda=2.394057
## + Fold03.Rep1: alpha=0.28799, lambda=0.824474
## - Fold03.Rep1: alpha=0.28799, lambda=0.824474
## + Fold03.Rep1: alpha=0.94218, lambda=2.531489
## - Fold03.Rep1: alpha=0.94218, lambda=2.531489
## + Fold03.Rep1: alpha=0.35679, lambda=1.223740
## - Fold03.Rep1: alpha=0.35679, lambda=1.223740
## + Fold03.Rep1: alpha=0.63956, lambda=3.222801
## - Fold03.Rep1: alpha=0.63956, lambda=3.222801
## + Fold03.Rep1: alpha=0.65727, lambda=0.001635
## - Fold03.Rep1: alpha=0.65727, lambda=0.001635
## + Fold03.Rep1: alpha=0.23136, lambda=0.011723
## - Fold03.Rep1: alpha=0.23136, lambda=0.011723
## + Fold03.Rep1: alpha=0.08606, lambda=0.018838
## - Fold03.Rep1: alpha=0.08606, lambda=0.018838
## + Fold03.Rep1: alpha=0.27970, lambda=0.518103
## - Fold03.Rep1: alpha=0.27970, lambda=0.518103
## + Fold04.Rep1: alpha=0.62989, lambda=0.003636
## - Fold04.Rep1: alpha=0.62989, lambda=0.003636
## + Fold04.Rep1: alpha=0.29776, lambda=2.394057
## - Fold04.Rep1: alpha=0.29776, lambda=2.394057
## + Fold04.Rep1: alpha=0.28799, lambda=0.824474
## - Fold04.Rep1: alpha=0.28799, lambda=0.824474
## + Fold04.Rep1: alpha=0.94218, lambda=2.531489
## - Fold04.Rep1: alpha=0.94218, lambda=2.531489
## + Fold04.Rep1: alpha=0.35679, lambda=1.223740
## - Fold04.Rep1: alpha=0.35679, lambda=1.223740
## + Fold04.Rep1: alpha=0.63956, lambda=3.222801
## - Fold04.Rep1: alpha=0.63956, lambda=3.222801
## + Fold04.Rep1: alpha=0.65727, lambda=0.001635
## - Fold04.Rep1: alpha=0.65727, lambda=0.001635
## + Fold04.Rep1: alpha=0.23136, lambda=0.011723
## - Fold04.Rep1: alpha=0.23136, lambda=0.011723
## + Fold04.Rep1: alpha=0.08606, lambda=0.018838
## - Fold04.Rep1: alpha=0.08606, lambda=0.018838
## + Fold04.Rep1: alpha=0.27970, lambda=0.518103
## - Fold04.Rep1: alpha=0.27970, lambda=0.518103
## + Fold05.Rep1: alpha=0.62989, lambda=0.003636
## - Fold05.Rep1: alpha=0.62989, lambda=0.003636
## + Fold05.Rep1: alpha=0.29776, lambda=2.394057
## - Fold05.Rep1: alpha=0.29776, lambda=2.394057
## + Fold05.Rep1: alpha=0.28799, lambda=0.824474
## - Fold05.Rep1: alpha=0.28799, lambda=0.824474
## + Fold05.Rep1: alpha=0.94218, lambda=2.531489
## - Fold05.Rep1: alpha=0.94218, lambda=2.531489
## + Fold05.Rep1: alpha=0.35679, lambda=1.223740
## - Fold05.Rep1: alpha=0.35679, lambda=1.223740
## + Fold05.Rep1: alpha=0.63956, lambda=3.222801
## - Fold05.Rep1: alpha=0.63956, lambda=3.222801
## + Fold05.Rep1: alpha=0.65727, lambda=0.001635
## - Fold05.Rep1: alpha=0.65727, lambda=0.001635
## + Fold05.Rep1: alpha=0.23136, lambda=0.011723
## - Fold05.Rep1: alpha=0.23136, lambda=0.011723
## + Fold05.Rep1: alpha=0.08606, lambda=0.018838
## - Fold05.Rep1: alpha=0.08606, lambda=0.018838
## + Fold05.Rep1: alpha=0.27970, lambda=0.518103
## - Fold05.Rep1: alpha=0.27970, lambda=0.518103
## + Fold06.Rep1: alpha=0.62989, lambda=0.003636
## - Fold06.Rep1: alpha=0.62989, lambda=0.003636
## + Fold06.Rep1: alpha=0.29776, lambda=2.394057
## - Fold06.Rep1: alpha=0.29776, lambda=2.394057
## + Fold06.Rep1: alpha=0.28799, lambda=0.824474
## - Fold06.Rep1: alpha=0.28799, lambda=0.824474
## + Fold06.Rep1: alpha=0.94218, lambda=2.531489
## - Fold06.Rep1: alpha=0.94218, lambda=2.531489
## + Fold06.Rep1: alpha=0.35679, lambda=1.223740
## - Fold06.Rep1: alpha=0.35679, lambda=1.223740
## + Fold06.Rep1: alpha=0.63956, lambda=3.222801
## - Fold06.Rep1: alpha=0.63956, lambda=3.222801
## + Fold06.Rep1: alpha=0.65727, lambda=0.001635
## - Fold06.Rep1: alpha=0.65727, lambda=0.001635
## + Fold06.Rep1: alpha=0.23136, lambda=0.011723
## - Fold06.Rep1: alpha=0.23136, lambda=0.011723
## + Fold06.Rep1: alpha=0.08606, lambda=0.018838
## - Fold06.Rep1: alpha=0.08606, lambda=0.018838
## + Fold06.Rep1: alpha=0.27970, lambda=0.518103
## - Fold06.Rep1: alpha=0.27970, lambda=0.518103
## + Fold07.Rep1: alpha=0.62989, lambda=0.003636
## - Fold07.Rep1: alpha=0.62989, lambda=0.003636
## + Fold07.Rep1: alpha=0.29776, lambda=2.394057
## - Fold07.Rep1: alpha=0.29776, lambda=2.394057
## + Fold07.Rep1: alpha=0.28799, lambda=0.824474
## - Fold07.Rep1: alpha=0.28799, lambda=0.824474
## + Fold07.Rep1: alpha=0.94218, lambda=2.531489
## - Fold07.Rep1: alpha=0.94218, lambda=2.531489
## + Fold07.Rep1: alpha=0.35679, lambda=1.223740
## - Fold07.Rep1: alpha=0.35679, lambda=1.223740
## + Fold07.Rep1: alpha=0.63956, lambda=3.222801
## - Fold07.Rep1: alpha=0.63956, lambda=3.222801
## + Fold07.Rep1: alpha=0.65727, lambda=0.001635
## - Fold07.Rep1: alpha=0.65727, lambda=0.001635
## + Fold07.Rep1: alpha=0.23136, lambda=0.011723
## - Fold07.Rep1: alpha=0.23136, lambda=0.011723
## + Fold07.Rep1: alpha=0.08606, lambda=0.018838
## - Fold07.Rep1: alpha=0.08606, lambda=0.018838
## + Fold07.Rep1: alpha=0.27970, lambda=0.518103
## - Fold07.Rep1: alpha=0.27970, lambda=0.518103
## + Fold08.Rep1: alpha=0.62989, lambda=0.003636
## - Fold08.Rep1: alpha=0.62989, lambda=0.003636
## + Fold08.Rep1: alpha=0.29776, lambda=2.394057
## - Fold08.Rep1: alpha=0.29776, lambda=2.394057
## + Fold08.Rep1: alpha=0.28799, lambda=0.824474
## - Fold08.Rep1: alpha=0.28799, lambda=0.824474
## + Fold08.Rep1: alpha=0.94218, lambda=2.531489
## - Fold08.Rep1: alpha=0.94218, lambda=2.531489
## + Fold08.Rep1: alpha=0.35679, lambda=1.223740
## - Fold08.Rep1: alpha=0.35679, lambda=1.223740
## + Fold08.Rep1: alpha=0.63956, lambda=3.222801
## - Fold08.Rep1: alpha=0.63956, lambda=3.222801
## + Fold08.Rep1: alpha=0.65727, lambda=0.001635
## - Fold08.Rep1: alpha=0.65727, lambda=0.001635
## + Fold08.Rep1: alpha=0.23136, lambda=0.011723
## - Fold08.Rep1: alpha=0.23136, lambda=0.011723
## + Fold08.Rep1: alpha=0.08606, lambda=0.018838
## - Fold08.Rep1: alpha=0.08606, lambda=0.018838
## + Fold08.Rep1: alpha=0.27970, lambda=0.518103
## - Fold08.Rep1: alpha=0.27970, lambda=0.518103
## + Fold09.Rep1: alpha=0.62989, lambda=0.003636
## - Fold09.Rep1: alpha=0.62989, lambda=0.003636
## + Fold09.Rep1: alpha=0.29776, lambda=2.394057
## - Fold09.Rep1: alpha=0.29776, lambda=2.394057
## + Fold09.Rep1: alpha=0.28799, lambda=0.824474
## - Fold09.Rep1: alpha=0.28799, lambda=0.824474
## + Fold09.Rep1: alpha=0.94218, lambda=2.531489
## - Fold09.Rep1: alpha=0.94218, lambda=2.531489
## + Fold09.Rep1: alpha=0.35679, lambda=1.223740
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## + Fold09.Rep1: alpha=0.63956, lambda=3.222801
## - Fold09.Rep1: alpha=0.63956, lambda=3.222801
## + Fold09.Rep1: alpha=0.65727, lambda=0.001635
## - Fold09.Rep1: alpha=0.65727, lambda=0.001635
## + Fold09.Rep1: alpha=0.23136, lambda=0.011723
## - Fold09.Rep1: alpha=0.23136, lambda=0.011723
## + Fold09.Rep1: alpha=0.08606, lambda=0.018838
## - Fold09.Rep1: alpha=0.08606, lambda=0.018838
## + Fold09.Rep1: alpha=0.27970, lambda=0.518103
## - Fold09.Rep1: alpha=0.27970, lambda=0.518103
## + Fold10.Rep1: alpha=0.62989, lambda=0.003636
## - Fold10.Rep1: alpha=0.62989, lambda=0.003636
## + Fold10.Rep1: alpha=0.29776, lambda=2.394057
## - Fold10.Rep1: alpha=0.29776, lambda=2.394057
## + Fold10.Rep1: alpha=0.28799, lambda=0.824474
## - Fold10.Rep1: alpha=0.28799, lambda=0.824474
## + Fold10.Rep1: alpha=0.94218, lambda=2.531489
## - Fold10.Rep1: alpha=0.94218, lambda=2.531489
## + Fold10.Rep1: alpha=0.35679, lambda=1.223740
## - Fold10.Rep1: alpha=0.35679, lambda=1.223740
## + Fold10.Rep1: alpha=0.63956, lambda=3.222801
## - Fold10.Rep1: alpha=0.63956, lambda=3.222801
## + Fold10.Rep1: alpha=0.65727, lambda=0.001635
## - Fold10.Rep1: alpha=0.65727, lambda=0.001635
## + Fold10.Rep1: alpha=0.23136, lambda=0.011723
## - Fold10.Rep1: alpha=0.23136, lambda=0.011723
## + Fold10.Rep1: alpha=0.08606, lambda=0.018838
## - Fold10.Rep1: alpha=0.08606, lambda=0.018838
## + Fold10.Rep1: alpha=0.27970, lambda=0.518103
## - Fold10.Rep1: alpha=0.27970, lambda=0.518103
## + Fold01.Rep2: alpha=0.62989, lambda=0.003636
## - Fold01.Rep2: alpha=0.62989, lambda=0.003636
## + Fold01.Rep2: alpha=0.29776, lambda=2.394057
## - Fold01.Rep2: alpha=0.29776, lambda=2.394057
## + Fold01.Rep2: alpha=0.28799, lambda=0.824474
## - Fold01.Rep2: alpha=0.28799, lambda=0.824474
## + Fold01.Rep2: alpha=0.94218, lambda=2.531489
## - Fold01.Rep2: alpha=0.94218, lambda=2.531489
## + Fold01.Rep2: alpha=0.35679, lambda=1.223740
## - Fold01.Rep2: alpha=0.35679, lambda=1.223740
## + Fold01.Rep2: alpha=0.63956, lambda=3.222801
## - Fold01.Rep2: alpha=0.63956, lambda=3.222801
## + Fold01.Rep2: alpha=0.65727, lambda=0.001635
## - Fold01.Rep2: alpha=0.65727, lambda=0.001635
## + Fold01.Rep2: alpha=0.23136, lambda=0.011723
## - Fold01.Rep2: alpha=0.23136, lambda=0.011723
## + Fold01.Rep2: alpha=0.08606, lambda=0.018838
## - Fold01.Rep2: alpha=0.08606, lambda=0.018838
## + Fold01.Rep2: alpha=0.27970, lambda=0.518103
## - Fold01.Rep2: alpha=0.27970, lambda=0.518103
## + Fold02.Rep2: alpha=0.62989, lambda=0.003636
## - Fold02.Rep2: alpha=0.62989, lambda=0.003636
## + Fold02.Rep2: alpha=0.29776, lambda=2.394057
## - Fold02.Rep2: alpha=0.29776, lambda=2.394057
## + Fold02.Rep2: alpha=0.28799, lambda=0.824474
## - Fold02.Rep2: alpha=0.28799, lambda=0.824474
## + Fold02.Rep2: alpha=0.94218, lambda=2.531489
## - Fold02.Rep2: alpha=0.94218, lambda=2.531489
## + Fold02.Rep2: alpha=0.35679, lambda=1.223740
## - Fold02.Rep2: alpha=0.35679, lambda=1.223740
## + Fold02.Rep2: alpha=0.63956, lambda=3.222801
## - Fold02.Rep2: alpha=0.63956, lambda=3.222801
## + Fold02.Rep2: alpha=0.65727, lambda=0.001635
## - Fold02.Rep2: alpha=0.65727, lambda=0.001635
## + Fold02.Rep2: alpha=0.23136, lambda=0.011723
## - Fold02.Rep2: alpha=0.23136, lambda=0.011723
## + Fold02.Rep2: alpha=0.08606, lambda=0.018838
## - Fold02.Rep2: alpha=0.08606, lambda=0.018838
## + Fold02.Rep2: alpha=0.27970, lambda=0.518103
## - Fold02.Rep2: alpha=0.27970, lambda=0.518103
## + Fold03.Rep2: alpha=0.62989, lambda=0.003636
## - Fold03.Rep2: alpha=0.62989, lambda=0.003636
## + Fold03.Rep2: alpha=0.29776, lambda=2.394057
## - Fold03.Rep2: alpha=0.29776, lambda=2.394057
## + Fold03.Rep2: alpha=0.28799, lambda=0.824474
## - Fold03.Rep2: alpha=0.28799, lambda=0.824474
## + Fold03.Rep2: alpha=0.94218, lambda=2.531489
## - Fold03.Rep2: alpha=0.94218, lambda=2.531489
## + Fold03.Rep2: alpha=0.35679, lambda=1.223740
## - Fold03.Rep2: alpha=0.35679, lambda=1.223740
## + Fold03.Rep2: alpha=0.63956, lambda=3.222801
## - Fold03.Rep2: alpha=0.63956, lambda=3.222801
## + Fold03.Rep2: alpha=0.65727, lambda=0.001635
## - Fold03.Rep2: alpha=0.65727, lambda=0.001635
## + Fold03.Rep2: alpha=0.23136, lambda=0.011723
## - Fold03.Rep2: alpha=0.23136, lambda=0.011723
## + Fold03.Rep2: alpha=0.08606, lambda=0.018838
## - Fold03.Rep2: alpha=0.08606, lambda=0.018838
## + Fold03.Rep2: alpha=0.27970, lambda=0.518103
## - Fold03.Rep2: alpha=0.27970, lambda=0.518103
## + Fold04.Rep2: alpha=0.62989, lambda=0.003636
## - Fold04.Rep2: alpha=0.62989, lambda=0.003636
## + Fold04.Rep2: alpha=0.29776, lambda=2.394057
## - Fold04.Rep2: alpha=0.29776, lambda=2.394057
## + Fold04.Rep2: alpha=0.28799, lambda=0.824474
## - Fold04.Rep2: alpha=0.28799, lambda=0.824474
## + Fold04.Rep2: alpha=0.94218, lambda=2.531489
## - Fold04.Rep2: alpha=0.94218, lambda=2.531489
## + Fold04.Rep2: alpha=0.35679, lambda=1.223740
## - Fold04.Rep2: alpha=0.35679, lambda=1.223740
## + Fold04.Rep2: alpha=0.63956, lambda=3.222801
## - Fold04.Rep2: alpha=0.63956, lambda=3.222801
## + Fold04.Rep2: alpha=0.65727, lambda=0.001635
## - Fold04.Rep2: alpha=0.65727, lambda=0.001635
## + Fold04.Rep2: alpha=0.23136, lambda=0.011723
## - Fold04.Rep2: alpha=0.23136, lambda=0.011723
## + Fold04.Rep2: alpha=0.08606, lambda=0.018838
## - Fold04.Rep2: alpha=0.08606, lambda=0.018838
## + Fold04.Rep2: alpha=0.27970, lambda=0.518103
## - Fold04.Rep2: alpha=0.27970, lambda=0.518103
## + Fold05.Rep2: alpha=0.62989, lambda=0.003636
## - Fold05.Rep2: alpha=0.62989, lambda=0.003636
## + Fold05.Rep2: alpha=0.29776, lambda=2.394057
## - Fold05.Rep2: alpha=0.29776, lambda=2.394057
## + Fold05.Rep2: alpha=0.28799, lambda=0.824474
## - Fold05.Rep2: alpha=0.28799, lambda=0.824474
## + Fold05.Rep2: alpha=0.94218, lambda=2.531489
## - Fold05.Rep2: alpha=0.94218, lambda=2.531489
## + Fold05.Rep2: alpha=0.35679, lambda=1.223740
## - Fold05.Rep2: alpha=0.35679, lambda=1.223740
## + Fold05.Rep2: alpha=0.63956, lambda=3.222801
## - Fold05.Rep2: alpha=0.63956, lambda=3.222801
## + Fold05.Rep2: alpha=0.65727, lambda=0.001635
## - Fold05.Rep2: alpha=0.65727, lambda=0.001635
## + Fold05.Rep2: alpha=0.23136, lambda=0.011723
## - Fold05.Rep2: alpha=0.23136, lambda=0.011723
## + Fold05.Rep2: alpha=0.08606, lambda=0.018838
## - Fold05.Rep2: alpha=0.08606, lambda=0.018838
## + Fold05.Rep2: alpha=0.27970, lambda=0.518103
## - Fold05.Rep2: alpha=0.27970, lambda=0.518103
## + Fold06.Rep2: alpha=0.62989, lambda=0.003636
## - Fold06.Rep2: alpha=0.62989, lambda=0.003636
## + Fold06.Rep2: alpha=0.29776, lambda=2.394057
## - Fold06.Rep2: alpha=0.29776, lambda=2.394057
## + Fold06.Rep2: alpha=0.28799, lambda=0.824474
## - Fold06.Rep2: alpha=0.28799, lambda=0.824474
## + Fold06.Rep2: alpha=0.94218, lambda=2.531489
## - Fold06.Rep2: alpha=0.94218, lambda=2.531489
## + Fold06.Rep2: alpha=0.35679, lambda=1.223740
## - Fold06.Rep2: alpha=0.35679, lambda=1.223740
## + Fold06.Rep2: alpha=0.63956, lambda=3.222801
## - Fold06.Rep2: alpha=0.63956, lambda=3.222801
## + Fold06.Rep2: alpha=0.65727, lambda=0.001635
## - Fold06.Rep2: alpha=0.65727, lambda=0.001635
## + Fold06.Rep2: alpha=0.23136, lambda=0.011723
## - Fold06.Rep2: alpha=0.23136, lambda=0.011723
## + Fold06.Rep2: alpha=0.08606, lambda=0.018838
## - Fold06.Rep2: alpha=0.08606, lambda=0.018838
## + Fold06.Rep2: alpha=0.27970, lambda=0.518103
## - Fold06.Rep2: alpha=0.27970, lambda=0.518103
## + Fold07.Rep2: alpha=0.62989, lambda=0.003636
## - Fold07.Rep2: alpha=0.62989, lambda=0.003636
## + Fold07.Rep2: alpha=0.29776, lambda=2.394057
## - Fold07.Rep2: alpha=0.29776, lambda=2.394057
## + Fold07.Rep2: alpha=0.28799, lambda=0.824474
## - Fold07.Rep2: alpha=0.28799, lambda=0.824474
## + Fold07.Rep2: alpha=0.94218, lambda=2.531489
## - Fold07.Rep2: alpha=0.94218, lambda=2.531489
## + Fold07.Rep2: alpha=0.35679, lambda=1.223740
## - Fold07.Rep2: alpha=0.35679, lambda=1.223740
## + Fold07.Rep2: alpha=0.63956, lambda=3.222801
## - Fold07.Rep2: alpha=0.63956, lambda=3.222801
## + Fold07.Rep2: alpha=0.65727, lambda=0.001635
## - Fold07.Rep2: alpha=0.65727, lambda=0.001635
## + Fold07.Rep2: alpha=0.23136, lambda=0.011723
## - Fold07.Rep2: alpha=0.23136, lambda=0.011723
## + Fold07.Rep2: alpha=0.08606, lambda=0.018838
## - Fold07.Rep2: alpha=0.08606, lambda=0.018838
## + Fold07.Rep2: alpha=0.27970, lambda=0.518103
## - Fold07.Rep2: alpha=0.27970, lambda=0.518103
## + Fold08.Rep2: alpha=0.62989, lambda=0.003636
## - Fold08.Rep2: alpha=0.62989, lambda=0.003636
## + Fold08.Rep2: alpha=0.29776, lambda=2.394057
## - Fold08.Rep2: alpha=0.29776, lambda=2.394057
## + Fold08.Rep2: alpha=0.28799, lambda=0.824474
## - Fold08.Rep2: alpha=0.28799, lambda=0.824474
## + Fold08.Rep2: alpha=0.94218, lambda=2.531489
## - Fold08.Rep2: alpha=0.94218, lambda=2.531489
## + Fold08.Rep2: alpha=0.35679, lambda=1.223740
## - Fold08.Rep2: alpha=0.35679, lambda=1.223740
## + Fold08.Rep2: alpha=0.63956, lambda=3.222801
## - Fold08.Rep2: alpha=0.63956, lambda=3.222801
## + Fold08.Rep2: alpha=0.65727, lambda=0.001635
## - Fold08.Rep2: alpha=0.65727, lambda=0.001635
## + Fold08.Rep2: alpha=0.23136, lambda=0.011723
## - Fold08.Rep2: alpha=0.23136, lambda=0.011723
## + Fold08.Rep2: alpha=0.08606, lambda=0.018838
## - Fold08.Rep2: alpha=0.08606, lambda=0.018838
## + Fold08.Rep2: alpha=0.27970, lambda=0.518103
## - Fold08.Rep2: alpha=0.27970, lambda=0.518103
## + Fold09.Rep2: alpha=0.62989, lambda=0.003636
## - Fold09.Rep2: alpha=0.62989, lambda=0.003636
## + Fold09.Rep2: alpha=0.29776, lambda=2.394057
## - Fold09.Rep2: alpha=0.29776, lambda=2.394057
## + Fold09.Rep2: alpha=0.28799, lambda=0.824474
## - Fold09.Rep2: alpha=0.28799, lambda=0.824474
## + Fold09.Rep2: alpha=0.94218, lambda=2.531489
## - Fold09.Rep2: alpha=0.94218, lambda=2.531489
## + Fold09.Rep2: alpha=0.35679, lambda=1.223740
## - Fold09.Rep2: alpha=0.35679, lambda=1.223740
## + Fold09.Rep2: alpha=0.63956, lambda=3.222801
## - Fold09.Rep2: alpha=0.63956, lambda=3.222801
## + Fold09.Rep2: alpha=0.65727, lambda=0.001635
## - Fold09.Rep2: alpha=0.65727, lambda=0.001635
## + Fold09.Rep2: alpha=0.23136, lambda=0.011723
## - Fold09.Rep2: alpha=0.23136, lambda=0.011723
## + Fold09.Rep2: alpha=0.08606, lambda=0.018838
## - Fold09.Rep2: alpha=0.08606, lambda=0.018838
## + Fold09.Rep2: alpha=0.27970, lambda=0.518103
## - Fold09.Rep2: alpha=0.27970, lambda=0.518103
## + Fold10.Rep2: alpha=0.62989, lambda=0.003636
## - Fold10.Rep2: alpha=0.62989, lambda=0.003636
## + Fold10.Rep2: alpha=0.29776, lambda=2.394057
## - Fold10.Rep2: alpha=0.29776, lambda=2.394057
## + Fold10.Rep2: alpha=0.28799, lambda=0.824474
## - Fold10.Rep2: alpha=0.28799, lambda=0.824474
## + Fold10.Rep2: alpha=0.94218, lambda=2.531489
## - Fold10.Rep2: alpha=0.94218, lambda=2.531489
## + Fold10.Rep2: alpha=0.35679, lambda=1.223740
## - Fold10.Rep2: alpha=0.35679, lambda=1.223740
## + Fold10.Rep2: alpha=0.63956, lambda=3.222801
## - Fold10.Rep2: alpha=0.63956, lambda=3.222801
## + Fold10.Rep2: alpha=0.65727, lambda=0.001635
## - Fold10.Rep2: alpha=0.65727, lambda=0.001635
## + Fold10.Rep2: alpha=0.23136, lambda=0.011723
## - Fold10.Rep2: alpha=0.23136, lambda=0.011723
## + Fold10.Rep2: alpha=0.08606, lambda=0.018838
## - Fold10.Rep2: alpha=0.08606, lambda=0.018838
## + Fold10.Rep2: alpha=0.27970, lambda=0.518103
## - Fold10.Rep2: alpha=0.27970, lambda=0.518103
## + Fold01.Rep3: alpha=0.62989, lambda=0.003636
## - Fold01.Rep3: alpha=0.62989, lambda=0.003636
## + Fold01.Rep3: alpha=0.29776, lambda=2.394057
## - Fold01.Rep3: alpha=0.29776, lambda=2.394057
## + Fold01.Rep3: alpha=0.28799, lambda=0.824474
## - Fold01.Rep3: alpha=0.28799, lambda=0.824474
## + Fold01.Rep3: alpha=0.94218, lambda=2.531489
## - Fold01.Rep3: alpha=0.94218, lambda=2.531489
## + Fold01.Rep3: alpha=0.35679, lambda=1.223740
## - Fold01.Rep3: alpha=0.35679, lambda=1.223740
## + Fold01.Rep3: alpha=0.63956, lambda=3.222801
## - Fold01.Rep3: alpha=0.63956, lambda=3.222801
## + Fold01.Rep3: alpha=0.65727, lambda=0.001635
## - Fold01.Rep3: alpha=0.65727, lambda=0.001635
## + Fold01.Rep3: alpha=0.23136, lambda=0.011723
## - Fold01.Rep3: alpha=0.23136, lambda=0.011723
## + Fold01.Rep3: alpha=0.08606, lambda=0.018838
## - Fold01.Rep3: alpha=0.08606, lambda=0.018838
## + Fold01.Rep3: alpha=0.27970, lambda=0.518103
## - Fold01.Rep3: alpha=0.27970, lambda=0.518103
## + Fold02.Rep3: alpha=0.62989, lambda=0.003636
## - Fold02.Rep3: alpha=0.62989, lambda=0.003636
## + Fold02.Rep3: alpha=0.29776, lambda=2.394057
## - Fold02.Rep3: alpha=0.29776, lambda=2.394057
## + Fold02.Rep3: alpha=0.28799, lambda=0.824474
## - Fold02.Rep3: alpha=0.28799, lambda=0.824474
## + Fold02.Rep3: alpha=0.94218, lambda=2.531489
## - Fold02.Rep3: alpha=0.94218, lambda=2.531489
## + Fold02.Rep3: alpha=0.35679, lambda=1.223740
## - Fold02.Rep3: alpha=0.35679, lambda=1.223740
## + Fold02.Rep3: alpha=0.63956, lambda=3.222801
## - Fold02.Rep3: alpha=0.63956, lambda=3.222801
## + Fold02.Rep3: alpha=0.65727, lambda=0.001635
## - Fold02.Rep3: alpha=0.65727, lambda=0.001635
## + Fold02.Rep3: alpha=0.23136, lambda=0.011723
## - Fold02.Rep3: alpha=0.23136, lambda=0.011723
## + Fold02.Rep3: alpha=0.08606, lambda=0.018838
## - Fold02.Rep3: alpha=0.08606, lambda=0.018838
## + Fold02.Rep3: alpha=0.27970, lambda=0.518103
## - Fold02.Rep3: alpha=0.27970, lambda=0.518103
## + Fold03.Rep3: alpha=0.62989, lambda=0.003636
## - Fold03.Rep3: alpha=0.62989, lambda=0.003636
## + Fold03.Rep3: alpha=0.29776, lambda=2.394057
## - Fold03.Rep3: alpha=0.29776, lambda=2.394057
## + Fold03.Rep3: alpha=0.28799, lambda=0.824474
## - Fold03.Rep3: alpha=0.28799, lambda=0.824474
## + Fold03.Rep3: alpha=0.94218, lambda=2.531489
## - Fold03.Rep3: alpha=0.94218, lambda=2.531489
## + Fold03.Rep3: alpha=0.35679, lambda=1.223740
## - Fold03.Rep3: alpha=0.35679, lambda=1.223740
## + Fold03.Rep3: alpha=0.63956, lambda=3.222801
## - Fold03.Rep3: alpha=0.63956, lambda=3.222801
## + Fold03.Rep3: alpha=0.65727, lambda=0.001635
## - Fold03.Rep3: alpha=0.65727, lambda=0.001635
## + Fold03.Rep3: alpha=0.23136, lambda=0.011723
## - Fold03.Rep3: alpha=0.23136, lambda=0.011723
## + Fold03.Rep3: alpha=0.08606, lambda=0.018838
## - Fold03.Rep3: alpha=0.08606, lambda=0.018838
## + Fold03.Rep3: alpha=0.27970, lambda=0.518103
## - Fold03.Rep3: alpha=0.27970, lambda=0.518103
## + Fold04.Rep3: alpha=0.62989, lambda=0.003636
## - Fold04.Rep3: alpha=0.62989, lambda=0.003636
## + Fold04.Rep3: alpha=0.29776, lambda=2.394057
## - Fold04.Rep3: alpha=0.29776, lambda=2.394057
## + Fold04.Rep3: alpha=0.28799, lambda=0.824474
## - Fold04.Rep3: alpha=0.28799, lambda=0.824474
## + Fold04.Rep3: alpha=0.94218, lambda=2.531489
## - Fold04.Rep3: alpha=0.94218, lambda=2.531489
## + Fold04.Rep3: alpha=0.35679, lambda=1.223740
## - Fold04.Rep3: alpha=0.35679, lambda=1.223740
## + Fold04.Rep3: alpha=0.63956, lambda=3.222801
## - Fold04.Rep3: alpha=0.63956, lambda=3.222801
## + Fold04.Rep3: alpha=0.65727, lambda=0.001635
## - Fold04.Rep3: alpha=0.65727, lambda=0.001635
## + Fold04.Rep3: alpha=0.23136, lambda=0.011723
## - Fold04.Rep3: alpha=0.23136, lambda=0.011723
## + Fold04.Rep3: alpha=0.08606, lambda=0.018838
## - Fold04.Rep3: alpha=0.08606, lambda=0.018838
## + Fold04.Rep3: alpha=0.27970, lambda=0.518103
## - Fold04.Rep3: alpha=0.27970, lambda=0.518103
## + Fold05.Rep3: alpha=0.62989, lambda=0.003636
## - Fold05.Rep3: alpha=0.62989, lambda=0.003636
## + Fold05.Rep3: alpha=0.29776, lambda=2.394057
## - Fold05.Rep3: alpha=0.29776, lambda=2.394057
## + Fold05.Rep3: alpha=0.28799, lambda=0.824474
## - Fold05.Rep3: alpha=0.28799, lambda=0.824474
## + Fold05.Rep3: alpha=0.94218, lambda=2.531489
## - Fold05.Rep3: alpha=0.94218, lambda=2.531489
## + Fold05.Rep3: alpha=0.35679, lambda=1.223740
## - Fold05.Rep3: alpha=0.35679, lambda=1.223740
## + Fold05.Rep3: alpha=0.63956, lambda=3.222801
## - Fold05.Rep3: alpha=0.63956, lambda=3.222801
## + Fold05.Rep3: alpha=0.65727, lambda=0.001635
## - Fold05.Rep3: alpha=0.65727, lambda=0.001635
## + Fold05.Rep3: alpha=0.23136, lambda=0.011723
## - Fold05.Rep3: alpha=0.23136, lambda=0.011723
## + Fold05.Rep3: alpha=0.08606, lambda=0.018838
## - Fold05.Rep3: alpha=0.08606, lambda=0.018838
## + Fold05.Rep3: alpha=0.27970, lambda=0.518103
## - Fold05.Rep3: alpha=0.27970, lambda=0.518103
## + Fold06.Rep3: alpha=0.62989, lambda=0.003636
## - Fold06.Rep3: alpha=0.62989, lambda=0.003636
## + Fold06.Rep3: alpha=0.29776, lambda=2.394057
## - Fold06.Rep3: alpha=0.29776, lambda=2.394057
## + Fold06.Rep3: alpha=0.28799, lambda=0.824474
## - Fold06.Rep3: alpha=0.28799, lambda=0.824474
## + Fold06.Rep3: alpha=0.94218, lambda=2.531489
## - Fold06.Rep3: alpha=0.94218, lambda=2.531489
## + Fold06.Rep3: alpha=0.35679, lambda=1.223740
## - Fold06.Rep3: alpha=0.35679, lambda=1.223740
## + Fold06.Rep3: alpha=0.63956, lambda=3.222801
## - Fold06.Rep3: alpha=0.63956, lambda=3.222801
## + Fold06.Rep3: alpha=0.65727, lambda=0.001635
## - Fold06.Rep3: alpha=0.65727, lambda=0.001635
## + Fold06.Rep3: alpha=0.23136, lambda=0.011723
## - Fold06.Rep3: alpha=0.23136, lambda=0.011723
## + Fold06.Rep3: alpha=0.08606, lambda=0.018838
## - Fold06.Rep3: alpha=0.08606, lambda=0.018838
## + Fold06.Rep3: alpha=0.27970, lambda=0.518103
## - Fold06.Rep3: alpha=0.27970, lambda=0.518103
## + Fold07.Rep3: alpha=0.62989, lambda=0.003636
## - Fold07.Rep3: alpha=0.62989, lambda=0.003636
## + Fold07.Rep3: alpha=0.29776, lambda=2.394057
## - Fold07.Rep3: alpha=0.29776, lambda=2.394057
## + Fold07.Rep3: alpha=0.28799, lambda=0.824474
## - Fold07.Rep3: alpha=0.28799, lambda=0.824474
## + Fold07.Rep3: alpha=0.94218, lambda=2.531489
## - Fold07.Rep3: alpha=0.94218, lambda=2.531489
## + Fold07.Rep3: alpha=0.35679, lambda=1.223740
## - Fold07.Rep3: alpha=0.35679, lambda=1.223740
## + Fold07.Rep3: alpha=0.63956, lambda=3.222801
## - Fold07.Rep3: alpha=0.63956, lambda=3.222801
## + Fold07.Rep3: alpha=0.65727, lambda=0.001635
## - Fold07.Rep3: alpha=0.65727, lambda=0.001635
## + Fold07.Rep3: alpha=0.23136, lambda=0.011723
## - Fold07.Rep3: alpha=0.23136, lambda=0.011723
## + Fold07.Rep3: alpha=0.08606, lambda=0.018838
## - Fold07.Rep3: alpha=0.08606, lambda=0.018838
## + Fold07.Rep3: alpha=0.27970, lambda=0.518103
## - Fold07.Rep3: alpha=0.27970, lambda=0.518103
## + Fold08.Rep3: alpha=0.62989, lambda=0.003636
## - Fold08.Rep3: alpha=0.62989, lambda=0.003636
## + Fold08.Rep3: alpha=0.29776, lambda=2.394057
## - Fold08.Rep3: alpha=0.29776, lambda=2.394057
## + Fold08.Rep3: alpha=0.28799, lambda=0.824474
## - Fold08.Rep3: alpha=0.28799, lambda=0.824474
## + Fold08.Rep3: alpha=0.94218, lambda=2.531489
## - Fold08.Rep3: alpha=0.94218, lambda=2.531489
## + Fold08.Rep3: alpha=0.35679, lambda=1.223740
## - Fold08.Rep3: alpha=0.35679, lambda=1.223740
## + Fold08.Rep3: alpha=0.63956, lambda=3.222801
## - Fold08.Rep3: alpha=0.63956, lambda=3.222801
## + Fold08.Rep3: alpha=0.65727, lambda=0.001635
## - Fold08.Rep3: alpha=0.65727, lambda=0.001635
## + Fold08.Rep3: alpha=0.23136, lambda=0.011723
## - Fold08.Rep3: alpha=0.23136, lambda=0.011723
## + Fold08.Rep3: alpha=0.08606, lambda=0.018838
## - Fold08.Rep3: alpha=0.08606, lambda=0.018838
## + Fold08.Rep3: alpha=0.27970, lambda=0.518103
## - Fold08.Rep3: alpha=0.27970, lambda=0.518103
## + Fold09.Rep3: alpha=0.62989, lambda=0.003636
## - Fold09.Rep3: alpha=0.62989, lambda=0.003636
## + Fold09.Rep3: alpha=0.29776, lambda=2.394057
## - Fold09.Rep3: alpha=0.29776, lambda=2.394057
## + Fold09.Rep3: alpha=0.28799, lambda=0.824474
## - Fold09.Rep3: alpha=0.28799, lambda=0.824474
## + Fold09.Rep3: alpha=0.94218, lambda=2.531489
## - Fold09.Rep3: alpha=0.94218, lambda=2.531489
## + Fold09.Rep3: alpha=0.35679, lambda=1.223740
## - Fold09.Rep3: alpha=0.35679, lambda=1.223740
## + Fold09.Rep3: alpha=0.63956, lambda=3.222801
## - Fold09.Rep3: alpha=0.63956, lambda=3.222801
## + Fold09.Rep3: alpha=0.65727, lambda=0.001635
## - Fold09.Rep3: alpha=0.65727, lambda=0.001635
## + Fold09.Rep3: alpha=0.23136, lambda=0.011723
## - Fold09.Rep3: alpha=0.23136, lambda=0.011723
## + Fold09.Rep3: alpha=0.08606, lambda=0.018838
## - Fold09.Rep3: alpha=0.08606, lambda=0.018838
## + Fold09.Rep3: alpha=0.27970, lambda=0.518103
## - Fold09.Rep3: alpha=0.27970, lambda=0.518103
## + Fold10.Rep3: alpha=0.62989, lambda=0.003636
## - Fold10.Rep3: alpha=0.62989, lambda=0.003636
## + Fold10.Rep3: alpha=0.29776, lambda=2.394057
## - Fold10.Rep3: alpha=0.29776, lambda=2.394057
## + Fold10.Rep3: alpha=0.28799, lambda=0.824474
## - Fold10.Rep3: alpha=0.28799, lambda=0.824474
## + Fold10.Rep3: alpha=0.94218, lambda=2.531489
## - Fold10.Rep3: alpha=0.94218, lambda=2.531489
## + Fold10.Rep3: alpha=0.35679, lambda=1.223740
## - Fold10.Rep3: alpha=0.35679, lambda=1.223740
## + Fold10.Rep3: alpha=0.63956, lambda=3.222801
## - Fold10.Rep3: alpha=0.63956, lambda=3.222801
## + Fold10.Rep3: alpha=0.65727, lambda=0.001635
## - Fold10.Rep3: alpha=0.65727, lambda=0.001635
## + Fold10.Rep3: alpha=0.23136, lambda=0.011723
## - Fold10.Rep3: alpha=0.23136, lambda=0.011723
## + Fold10.Rep3: alpha=0.08606, lambda=0.018838
## - Fold10.Rep3: alpha=0.08606, lambda=0.018838
## + Fold10.Rep3: alpha=0.27970, lambda=0.518103
## - Fold10.Rep3: alpha=0.27970, lambda=0.518103
## + Fold01.Rep4: alpha=0.62989, lambda=0.003636
## - Fold01.Rep4: alpha=0.62989, lambda=0.003636
## + Fold01.Rep4: alpha=0.29776, lambda=2.394057
## - Fold01.Rep4: alpha=0.29776, lambda=2.394057
## + Fold01.Rep4: alpha=0.28799, lambda=0.824474
## - Fold01.Rep4: alpha=0.28799, lambda=0.824474
## + Fold01.Rep4: alpha=0.94218, lambda=2.531489
## - Fold01.Rep4: alpha=0.94218, lambda=2.531489
## + Fold01.Rep4: alpha=0.35679, lambda=1.223740
## - Fold01.Rep4: alpha=0.35679, lambda=1.223740
## + Fold01.Rep4: alpha=0.63956, lambda=3.222801
## - Fold01.Rep4: alpha=0.63956, lambda=3.222801
## + Fold01.Rep4: alpha=0.65727, lambda=0.001635
## - Fold01.Rep4: alpha=0.65727, lambda=0.001635
## + Fold01.Rep4: alpha=0.23136, lambda=0.011723
## - Fold01.Rep4: alpha=0.23136, lambda=0.011723
## + Fold01.Rep4: alpha=0.08606, lambda=0.018838
## - Fold01.Rep4: alpha=0.08606, lambda=0.018838
## + Fold01.Rep4: alpha=0.27970, lambda=0.518103
## - Fold01.Rep4: alpha=0.27970, lambda=0.518103
## + Fold02.Rep4: alpha=0.62989, lambda=0.003636
## - Fold02.Rep4: alpha=0.62989, lambda=0.003636
## + Fold02.Rep4: alpha=0.29776, lambda=2.394057
## - Fold02.Rep4: alpha=0.29776, lambda=2.394057
## + Fold02.Rep4: alpha=0.28799, lambda=0.824474
## - Fold02.Rep4: alpha=0.28799, lambda=0.824474
## + Fold02.Rep4: alpha=0.94218, lambda=2.531489
## - Fold02.Rep4: alpha=0.94218, lambda=2.531489
## + Fold02.Rep4: alpha=0.35679, lambda=1.223740
## - Fold02.Rep4: alpha=0.35679, lambda=1.223740
## + Fold02.Rep4: alpha=0.63956, lambda=3.222801
## - Fold02.Rep4: alpha=0.63956, lambda=3.222801
## + Fold02.Rep4: alpha=0.65727, lambda=0.001635
## - Fold02.Rep4: alpha=0.65727, lambda=0.001635
## + Fold02.Rep4: alpha=0.23136, lambda=0.011723
## - Fold02.Rep4: alpha=0.23136, lambda=0.011723
## + Fold02.Rep4: alpha=0.08606, lambda=0.018838
## - Fold02.Rep4: alpha=0.08606, lambda=0.018838
## + Fold02.Rep4: alpha=0.27970, lambda=0.518103
## - Fold02.Rep4: alpha=0.27970, lambda=0.518103
## + Fold03.Rep4: alpha=0.62989, lambda=0.003636
## - Fold03.Rep4: alpha=0.62989, lambda=0.003636
## + Fold03.Rep4: alpha=0.29776, lambda=2.394057
## - Fold03.Rep4: alpha=0.29776, lambda=2.394057
## + Fold03.Rep4: alpha=0.28799, lambda=0.824474
## - Fold03.Rep4: alpha=0.28799, lambda=0.824474
## + Fold03.Rep4: alpha=0.94218, lambda=2.531489
## - Fold03.Rep4: alpha=0.94218, lambda=2.531489
## + Fold03.Rep4: alpha=0.35679, lambda=1.223740
## - Fold03.Rep4: alpha=0.35679, lambda=1.223740
## + Fold03.Rep4: alpha=0.63956, lambda=3.222801
## - Fold03.Rep4: alpha=0.63956, lambda=3.222801
## + Fold03.Rep4: alpha=0.65727, lambda=0.001635
## - Fold03.Rep4: alpha=0.65727, lambda=0.001635
## + Fold03.Rep4: alpha=0.23136, lambda=0.011723
## - Fold03.Rep4: alpha=0.23136, lambda=0.011723
## + Fold03.Rep4: alpha=0.08606, lambda=0.018838
## - Fold03.Rep4: alpha=0.08606, lambda=0.018838
## + Fold03.Rep4: alpha=0.27970, lambda=0.518103
## - Fold03.Rep4: alpha=0.27970, lambda=0.518103
## + Fold04.Rep4: alpha=0.62989, lambda=0.003636
## - Fold04.Rep4: alpha=0.62989, lambda=0.003636
## + Fold04.Rep4: alpha=0.29776, lambda=2.394057
## - Fold04.Rep4: alpha=0.29776, lambda=2.394057
## + Fold04.Rep4: alpha=0.28799, lambda=0.824474
## - Fold04.Rep4: alpha=0.28799, lambda=0.824474
## + Fold04.Rep4: alpha=0.94218, lambda=2.531489
## - Fold04.Rep4: alpha=0.94218, lambda=2.531489
## + Fold04.Rep4: alpha=0.35679, lambda=1.223740
## - Fold04.Rep4: alpha=0.35679, lambda=1.223740
## + Fold04.Rep4: alpha=0.63956, lambda=3.222801
## - Fold04.Rep4: alpha=0.63956, lambda=3.222801
## + Fold04.Rep4: alpha=0.65727, lambda=0.001635
## - Fold04.Rep4: alpha=0.65727, lambda=0.001635
## + Fold04.Rep4: alpha=0.23136, lambda=0.011723
## - Fold04.Rep4: alpha=0.23136, lambda=0.011723
## + Fold04.Rep4: alpha=0.08606, lambda=0.018838
## - Fold04.Rep4: alpha=0.08606, lambda=0.018838
## + Fold04.Rep4: alpha=0.27970, lambda=0.518103
## - Fold04.Rep4: alpha=0.27970, lambda=0.518103
## + Fold05.Rep4: alpha=0.62989, lambda=0.003636
## - Fold05.Rep4: alpha=0.62989, lambda=0.003636
## + Fold05.Rep4: alpha=0.29776, lambda=2.394057
## - Fold05.Rep4: alpha=0.29776, lambda=2.394057
## + Fold05.Rep4: alpha=0.28799, lambda=0.824474
## - Fold05.Rep4: alpha=0.28799, lambda=0.824474
## + Fold05.Rep4: alpha=0.94218, lambda=2.531489
## - Fold05.Rep4: alpha=0.94218, lambda=2.531489
## + Fold05.Rep4: alpha=0.35679, lambda=1.223740
## - Fold05.Rep4: alpha=0.35679, lambda=1.223740
## + Fold05.Rep4: alpha=0.63956, lambda=3.222801
## - Fold05.Rep4: alpha=0.63956, lambda=3.222801
## + Fold05.Rep4: alpha=0.65727, lambda=0.001635
## - Fold05.Rep4: alpha=0.65727, lambda=0.001635
## + Fold05.Rep4: alpha=0.23136, lambda=0.011723
## - Fold05.Rep4: alpha=0.23136, lambda=0.011723
## + Fold05.Rep4: alpha=0.08606, lambda=0.018838
## - Fold05.Rep4: alpha=0.08606, lambda=0.018838
## + Fold05.Rep4: alpha=0.27970, lambda=0.518103
## - Fold05.Rep4: alpha=0.27970, lambda=0.518103
## + Fold06.Rep4: alpha=0.62989, lambda=0.003636
## - Fold06.Rep4: alpha=0.62989, lambda=0.003636
## + Fold06.Rep4: alpha=0.29776, lambda=2.394057
## - Fold06.Rep4: alpha=0.29776, lambda=2.394057
## + Fold06.Rep4: alpha=0.28799, lambda=0.824474
## - Fold06.Rep4: alpha=0.28799, lambda=0.824474
## + Fold06.Rep4: alpha=0.94218, lambda=2.531489
## - Fold06.Rep4: alpha=0.94218, lambda=2.531489
## + Fold06.Rep4: alpha=0.35679, lambda=1.223740
## - Fold06.Rep4: alpha=0.35679, lambda=1.223740
## + Fold06.Rep4: alpha=0.63956, lambda=3.222801
## - Fold06.Rep4: alpha=0.63956, lambda=3.222801
## + Fold06.Rep4: alpha=0.65727, lambda=0.001635
## - Fold06.Rep4: alpha=0.65727, lambda=0.001635
## + Fold06.Rep4: alpha=0.23136, lambda=0.011723
## - Fold06.Rep4: alpha=0.23136, lambda=0.011723
## + Fold06.Rep4: alpha=0.08606, lambda=0.018838
## - Fold06.Rep4: alpha=0.08606, lambda=0.018838
## + Fold06.Rep4: alpha=0.27970, lambda=0.518103
## - Fold06.Rep4: alpha=0.27970, lambda=0.518103
## + Fold07.Rep4: alpha=0.62989, lambda=0.003636
## - Fold07.Rep4: alpha=0.62989, lambda=0.003636
## + Fold07.Rep4: alpha=0.29776, lambda=2.394057
## - Fold07.Rep4: alpha=0.29776, lambda=2.394057
## + Fold07.Rep4: alpha=0.28799, lambda=0.824474
## - Fold07.Rep4: alpha=0.28799, lambda=0.824474
## + Fold07.Rep4: alpha=0.94218, lambda=2.531489
## - Fold07.Rep4: alpha=0.94218, lambda=2.531489
## + Fold07.Rep4: alpha=0.35679, lambda=1.223740
## - Fold07.Rep4: alpha=0.35679, lambda=1.223740
## + Fold07.Rep4: alpha=0.63956, lambda=3.222801
## - Fold07.Rep4: alpha=0.63956, lambda=3.222801
## + Fold07.Rep4: alpha=0.65727, lambda=0.001635
## - Fold07.Rep4: alpha=0.65727, lambda=0.001635
## + Fold07.Rep4: alpha=0.23136, lambda=0.011723
## - Fold07.Rep4: alpha=0.23136, lambda=0.011723
## + Fold07.Rep4: alpha=0.08606, lambda=0.018838
## - Fold07.Rep4: alpha=0.08606, lambda=0.018838
## + Fold07.Rep4: alpha=0.27970, lambda=0.518103
## - Fold07.Rep4: alpha=0.27970, lambda=0.518103
## + Fold08.Rep4: alpha=0.62989, lambda=0.003636
## - Fold08.Rep4: alpha=0.62989, lambda=0.003636
## + Fold08.Rep4: alpha=0.29776, lambda=2.394057
## - Fold08.Rep4: alpha=0.29776, lambda=2.394057
## + Fold08.Rep4: alpha=0.28799, lambda=0.824474
## - Fold08.Rep4: alpha=0.28799, lambda=0.824474
## + Fold08.Rep4: alpha=0.94218, lambda=2.531489
## - Fold08.Rep4: alpha=0.94218, lambda=2.531489
## + Fold08.Rep4: alpha=0.35679, lambda=1.223740
## - Fold08.Rep4: alpha=0.35679, lambda=1.223740
## + Fold08.Rep4: alpha=0.63956, lambda=3.222801
## - Fold08.Rep4: alpha=0.63956, lambda=3.222801
## + Fold08.Rep4: alpha=0.65727, lambda=0.001635
## - Fold08.Rep4: alpha=0.65727, lambda=0.001635
## + Fold08.Rep4: alpha=0.23136, lambda=0.011723
## - Fold08.Rep4: alpha=0.23136, lambda=0.011723
## + Fold08.Rep4: alpha=0.08606, lambda=0.018838
## - Fold08.Rep4: alpha=0.08606, lambda=0.018838
## + Fold08.Rep4: alpha=0.27970, lambda=0.518103
## - Fold08.Rep4: alpha=0.27970, lambda=0.518103
## + Fold09.Rep4: alpha=0.62989, lambda=0.003636
## - Fold09.Rep4: alpha=0.62989, lambda=0.003636
## + Fold09.Rep4: alpha=0.29776, lambda=2.394057
## - Fold09.Rep4: alpha=0.29776, lambda=2.394057
## + Fold09.Rep4: alpha=0.28799, lambda=0.824474
## - Fold09.Rep4: alpha=0.28799, lambda=0.824474
## + Fold09.Rep4: alpha=0.94218, lambda=2.531489
## - Fold09.Rep4: alpha=0.94218, lambda=2.531489
## + Fold09.Rep4: alpha=0.35679, lambda=1.223740
## - Fold09.Rep4: alpha=0.35679, lambda=1.223740
## + Fold09.Rep4: alpha=0.63956, lambda=3.222801
## - Fold09.Rep4: alpha=0.63956, lambda=3.222801
## + Fold09.Rep4: alpha=0.65727, lambda=0.001635
## - Fold09.Rep4: alpha=0.65727, lambda=0.001635
## + Fold09.Rep4: alpha=0.23136, lambda=0.011723
## - Fold09.Rep4: alpha=0.23136, lambda=0.011723
## + Fold09.Rep4: alpha=0.08606, lambda=0.018838
## - Fold09.Rep4: alpha=0.08606, lambda=0.018838
## + Fold09.Rep4: alpha=0.27970, lambda=0.518103
## - Fold09.Rep4: alpha=0.27970, lambda=0.518103
## + Fold10.Rep4: alpha=0.62989, lambda=0.003636
## - Fold10.Rep4: alpha=0.62989, lambda=0.003636
## + Fold10.Rep4: alpha=0.29776, lambda=2.394057
## - Fold10.Rep4: alpha=0.29776, lambda=2.394057
## + Fold10.Rep4: alpha=0.28799, lambda=0.824474
## - Fold10.Rep4: alpha=0.28799, lambda=0.824474
## + Fold10.Rep4: alpha=0.94218, lambda=2.531489
## - Fold10.Rep4: alpha=0.94218, lambda=2.531489
## + Fold10.Rep4: alpha=0.35679, lambda=1.223740
## - Fold10.Rep4: alpha=0.35679, lambda=1.223740
## + Fold10.Rep4: alpha=0.63956, lambda=3.222801
## - Fold10.Rep4: alpha=0.63956, lambda=3.222801
## + Fold10.Rep4: alpha=0.65727, lambda=0.001635
## - Fold10.Rep4: alpha=0.65727, lambda=0.001635
## + Fold10.Rep4: alpha=0.23136, lambda=0.011723
## - Fold10.Rep4: alpha=0.23136, lambda=0.011723
## + Fold10.Rep4: alpha=0.08606, lambda=0.018838
## - Fold10.Rep4: alpha=0.08606, lambda=0.018838
## + Fold10.Rep4: alpha=0.27970, lambda=0.518103
## - Fold10.Rep4: alpha=0.27970, lambda=0.518103
## + Fold01.Rep5: alpha=0.62989, lambda=0.003636
## - Fold01.Rep5: alpha=0.62989, lambda=0.003636
## + Fold01.Rep5: alpha=0.29776, lambda=2.394057
## - Fold01.Rep5: alpha=0.29776, lambda=2.394057
## + Fold01.Rep5: alpha=0.28799, lambda=0.824474
## - Fold01.Rep5: alpha=0.28799, lambda=0.824474
## + Fold01.Rep5: alpha=0.94218, lambda=2.531489
## - Fold01.Rep5: alpha=0.94218, lambda=2.531489
## + Fold01.Rep5: alpha=0.35679, lambda=1.223740
## - Fold01.Rep5: alpha=0.35679, lambda=1.223740
## + Fold01.Rep5: alpha=0.63956, lambda=3.222801
## - Fold01.Rep5: alpha=0.63956, lambda=3.222801
## + Fold01.Rep5: alpha=0.65727, lambda=0.001635
## - Fold01.Rep5: alpha=0.65727, lambda=0.001635
## + Fold01.Rep5: alpha=0.23136, lambda=0.011723
## - Fold01.Rep5: alpha=0.23136, lambda=0.011723
## + Fold01.Rep5: alpha=0.08606, lambda=0.018838
## - Fold01.Rep5: alpha=0.08606, lambda=0.018838
## + Fold01.Rep5: alpha=0.27970, lambda=0.518103
## - Fold01.Rep5: alpha=0.27970, lambda=0.518103
## + Fold02.Rep5: alpha=0.62989, lambda=0.003636
## - Fold02.Rep5: alpha=0.62989, lambda=0.003636
## + Fold02.Rep5: alpha=0.29776, lambda=2.394057
## - Fold02.Rep5: alpha=0.29776, lambda=2.394057
## + Fold02.Rep5: alpha=0.28799, lambda=0.824474
## - Fold02.Rep5: alpha=0.28799, lambda=0.824474
## + Fold02.Rep5: alpha=0.94218, lambda=2.531489
## - Fold02.Rep5: alpha=0.94218, lambda=2.531489
## + Fold02.Rep5: alpha=0.35679, lambda=1.223740
## - Fold02.Rep5: alpha=0.35679, lambda=1.223740
## + Fold02.Rep5: alpha=0.63956, lambda=3.222801
## - Fold02.Rep5: alpha=0.63956, lambda=3.222801
## + Fold02.Rep5: alpha=0.65727, lambda=0.001635
## - Fold02.Rep5: alpha=0.65727, lambda=0.001635
## + Fold02.Rep5: alpha=0.23136, lambda=0.011723
## - Fold02.Rep5: alpha=0.23136, lambda=0.011723
## + Fold02.Rep5: alpha=0.08606, lambda=0.018838
## - Fold02.Rep5: alpha=0.08606, lambda=0.018838
## + Fold02.Rep5: alpha=0.27970, lambda=0.518103
## - Fold02.Rep5: alpha=0.27970, lambda=0.518103
## + Fold03.Rep5: alpha=0.62989, lambda=0.003636
## - Fold03.Rep5: alpha=0.62989, lambda=0.003636
## + Fold03.Rep5: alpha=0.29776, lambda=2.394057
## - Fold03.Rep5: alpha=0.29776, lambda=2.394057
## + Fold03.Rep5: alpha=0.28799, lambda=0.824474
## - Fold03.Rep5: alpha=0.28799, lambda=0.824474
## + Fold03.Rep5: alpha=0.94218, lambda=2.531489
## - Fold03.Rep5: alpha=0.94218, lambda=2.531489
## + Fold03.Rep5: alpha=0.35679, lambda=1.223740
## - Fold03.Rep5: alpha=0.35679, lambda=1.223740
## + Fold03.Rep5: alpha=0.63956, lambda=3.222801
## - Fold03.Rep5: alpha=0.63956, lambda=3.222801
## + Fold03.Rep5: alpha=0.65727, lambda=0.001635
## - Fold03.Rep5: alpha=0.65727, lambda=0.001635
## + Fold03.Rep5: alpha=0.23136, lambda=0.011723
## - Fold03.Rep5: alpha=0.23136, lambda=0.011723
## + Fold03.Rep5: alpha=0.08606, lambda=0.018838
## - Fold03.Rep5: alpha=0.08606, lambda=0.018838
## + Fold03.Rep5: alpha=0.27970, lambda=0.518103
## - Fold03.Rep5: alpha=0.27970, lambda=0.518103
## + Fold04.Rep5: alpha=0.62989, lambda=0.003636
## - Fold04.Rep5: alpha=0.62989, lambda=0.003636
## + Fold04.Rep5: alpha=0.29776, lambda=2.394057
## - Fold04.Rep5: alpha=0.29776, lambda=2.394057
## + Fold04.Rep5: alpha=0.28799, lambda=0.824474
## - Fold04.Rep5: alpha=0.28799, lambda=0.824474
## + Fold04.Rep5: alpha=0.94218, lambda=2.531489
## - Fold04.Rep5: alpha=0.94218, lambda=2.531489
## + Fold04.Rep5: alpha=0.35679, lambda=1.223740
## - Fold04.Rep5: alpha=0.35679, lambda=1.223740
## + Fold04.Rep5: alpha=0.63956, lambda=3.222801
## - Fold04.Rep5: alpha=0.63956, lambda=3.222801
## + Fold04.Rep5: alpha=0.65727, lambda=0.001635
## - Fold04.Rep5: alpha=0.65727, lambda=0.001635
## + Fold04.Rep5: alpha=0.23136, lambda=0.011723
## - Fold04.Rep5: alpha=0.23136, lambda=0.011723
## + Fold04.Rep5: alpha=0.08606, lambda=0.018838
## - Fold04.Rep5: alpha=0.08606, lambda=0.018838
## + Fold04.Rep5: alpha=0.27970, lambda=0.518103
## - Fold04.Rep5: alpha=0.27970, lambda=0.518103
## + Fold05.Rep5: alpha=0.62989, lambda=0.003636
## - Fold05.Rep5: alpha=0.62989, lambda=0.003636
## + Fold05.Rep5: alpha=0.29776, lambda=2.394057
## - Fold05.Rep5: alpha=0.29776, lambda=2.394057
## + Fold05.Rep5: alpha=0.28799, lambda=0.824474
## - Fold05.Rep5: alpha=0.28799, lambda=0.824474
## + Fold05.Rep5: alpha=0.94218, lambda=2.531489
## - Fold05.Rep5: alpha=0.94218, lambda=2.531489
## + Fold05.Rep5: alpha=0.35679, lambda=1.223740
## - Fold05.Rep5: alpha=0.35679, lambda=1.223740
## + Fold05.Rep5: alpha=0.63956, lambda=3.222801
## - Fold05.Rep5: alpha=0.63956, lambda=3.222801
## + Fold05.Rep5: alpha=0.65727, lambda=0.001635
## - Fold05.Rep5: alpha=0.65727, lambda=0.001635
## + Fold05.Rep5: alpha=0.23136, lambda=0.011723
## - Fold05.Rep5: alpha=0.23136, lambda=0.011723
## + Fold05.Rep5: alpha=0.08606, lambda=0.018838
## - Fold05.Rep5: alpha=0.08606, lambda=0.018838
## + Fold05.Rep5: alpha=0.27970, lambda=0.518103
## - Fold05.Rep5: alpha=0.27970, lambda=0.518103
## + Fold06.Rep5: alpha=0.62989, lambda=0.003636
## - Fold06.Rep5: alpha=0.62989, lambda=0.003636
## + Fold06.Rep5: alpha=0.29776, lambda=2.394057
## - Fold06.Rep5: alpha=0.29776, lambda=2.394057
## + Fold06.Rep5: alpha=0.28799, lambda=0.824474
## - Fold06.Rep5: alpha=0.28799, lambda=0.824474
## + Fold06.Rep5: alpha=0.94218, lambda=2.531489
## - Fold06.Rep5: alpha=0.94218, lambda=2.531489
## + Fold06.Rep5: alpha=0.35679, lambda=1.223740
## - Fold06.Rep5: alpha=0.35679, lambda=1.223740
## + Fold06.Rep5: alpha=0.63956, lambda=3.222801
## - Fold06.Rep5: alpha=0.63956, lambda=3.222801
## + Fold06.Rep5: alpha=0.65727, lambda=0.001635
## - Fold06.Rep5: alpha=0.65727, lambda=0.001635
## + Fold06.Rep5: alpha=0.23136, lambda=0.011723
## - Fold06.Rep5: alpha=0.23136, lambda=0.011723
## + Fold06.Rep5: alpha=0.08606, lambda=0.018838
## - Fold06.Rep5: alpha=0.08606, lambda=0.018838
## + Fold06.Rep5: alpha=0.27970, lambda=0.518103
## - Fold06.Rep5: alpha=0.27970, lambda=0.518103
## + Fold07.Rep5: alpha=0.62989, lambda=0.003636
## - Fold07.Rep5: alpha=0.62989, lambda=0.003636
## + Fold07.Rep5: alpha=0.29776, lambda=2.394057
## - Fold07.Rep5: alpha=0.29776, lambda=2.394057
## + Fold07.Rep5: alpha=0.28799, lambda=0.824474
## - Fold07.Rep5: alpha=0.28799, lambda=0.824474
## + Fold07.Rep5: alpha=0.94218, lambda=2.531489
## - Fold07.Rep5: alpha=0.94218, lambda=2.531489
## + Fold07.Rep5: alpha=0.35679, lambda=1.223740
## - Fold07.Rep5: alpha=0.35679, lambda=1.223740
## + Fold07.Rep5: alpha=0.63956, lambda=3.222801
## - Fold07.Rep5: alpha=0.63956, lambda=3.222801
## + Fold07.Rep5: alpha=0.65727, lambda=0.001635
## - Fold07.Rep5: alpha=0.65727, lambda=0.001635
## + Fold07.Rep5: alpha=0.23136, lambda=0.011723
## - Fold07.Rep5: alpha=0.23136, lambda=0.011723
## + Fold07.Rep5: alpha=0.08606, lambda=0.018838
## - Fold07.Rep5: alpha=0.08606, lambda=0.018838
## + Fold07.Rep5: alpha=0.27970, lambda=0.518103
## - Fold07.Rep5: alpha=0.27970, lambda=0.518103
## + Fold08.Rep5: alpha=0.62989, lambda=0.003636
## - Fold08.Rep5: alpha=0.62989, lambda=0.003636
## + Fold08.Rep5: alpha=0.29776, lambda=2.394057
## - Fold08.Rep5: alpha=0.29776, lambda=2.394057
## + Fold08.Rep5: alpha=0.28799, lambda=0.824474
## - Fold08.Rep5: alpha=0.28799, lambda=0.824474
## + Fold08.Rep5: alpha=0.94218, lambda=2.531489
## - Fold08.Rep5: alpha=0.94218, lambda=2.531489
## + Fold08.Rep5: alpha=0.35679, lambda=1.223740
## - Fold08.Rep5: alpha=0.35679, lambda=1.223740
## + Fold08.Rep5: alpha=0.63956, lambda=3.222801
## - Fold08.Rep5: alpha=0.63956, lambda=3.222801
## + Fold08.Rep5: alpha=0.65727, lambda=0.001635
## - Fold08.Rep5: alpha=0.65727, lambda=0.001635
## + Fold08.Rep5: alpha=0.23136, lambda=0.011723
## - Fold08.Rep5: alpha=0.23136, lambda=0.011723
## + Fold08.Rep5: alpha=0.08606, lambda=0.018838
## - Fold08.Rep5: alpha=0.08606, lambda=0.018838
## + Fold08.Rep5: alpha=0.27970, lambda=0.518103
## - Fold08.Rep5: alpha=0.27970, lambda=0.518103
## + Fold09.Rep5: alpha=0.62989, lambda=0.003636
## - Fold09.Rep5: alpha=0.62989, lambda=0.003636
## + Fold09.Rep5: alpha=0.29776, lambda=2.394057
## - Fold09.Rep5: alpha=0.29776, lambda=2.394057
## + Fold09.Rep5: alpha=0.28799, lambda=0.824474
## - Fold09.Rep5: alpha=0.28799, lambda=0.824474
## + Fold09.Rep5: alpha=0.94218, lambda=2.531489
## - Fold09.Rep5: alpha=0.94218, lambda=2.531489
## + Fold09.Rep5: alpha=0.35679, lambda=1.223740
## - Fold09.Rep5: alpha=0.35679, lambda=1.223740
## + Fold09.Rep5: alpha=0.63956, lambda=3.222801
## - Fold09.Rep5: alpha=0.63956, lambda=3.222801
## + Fold09.Rep5: alpha=0.65727, lambda=0.001635
## - Fold09.Rep5: alpha=0.65727, lambda=0.001635
## + Fold09.Rep5: alpha=0.23136, lambda=0.011723
## - Fold09.Rep5: alpha=0.23136, lambda=0.011723
## + Fold09.Rep5: alpha=0.08606, lambda=0.018838
## - Fold09.Rep5: alpha=0.08606, lambda=0.018838
## + Fold09.Rep5: alpha=0.27970, lambda=0.518103
## - Fold09.Rep5: alpha=0.27970, lambda=0.518103
## + Fold10.Rep5: alpha=0.62989, lambda=0.003636
## - Fold10.Rep5: alpha=0.62989, lambda=0.003636
## + Fold10.Rep5: alpha=0.29776, lambda=2.394057
## - Fold10.Rep5: alpha=0.29776, lambda=2.394057
## + Fold10.Rep5: alpha=0.28799, lambda=0.824474
## - Fold10.Rep5: alpha=0.28799, lambda=0.824474
## + Fold10.Rep5: alpha=0.94218, lambda=2.531489
## - Fold10.Rep5: alpha=0.94218, lambda=2.531489
## + Fold10.Rep5: alpha=0.35679, lambda=1.223740
## - Fold10.Rep5: alpha=0.35679, lambda=1.223740
## + Fold10.Rep5: alpha=0.63956, lambda=3.222801
## - Fold10.Rep5: alpha=0.63956, lambda=3.222801
## + Fold10.Rep5: alpha=0.65727, lambda=0.001635
## - Fold10.Rep5: alpha=0.65727, lambda=0.001635
## + Fold10.Rep5: alpha=0.23136, lambda=0.011723
## - Fold10.Rep5: alpha=0.23136, lambda=0.011723
## + Fold10.Rep5: alpha=0.08606, lambda=0.018838
## - Fold10.Rep5: alpha=0.08606, lambda=0.018838
## + Fold10.Rep5: alpha=0.27970, lambda=0.518103
## - Fold10.Rep5: alpha=0.27970, lambda=0.518103
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.0861, lambda = 0.0188 on full training set
# Best tuning parameter
elastic_reg$bestTune
## alpha lambda
## 1 0.08605824 0.01883794
# Make predictions on training set
predictions_train <- predict(elastic_reg, x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6338215 0.3638118
# Make predictions on test set
predictions_test <- predict(elastic_reg, x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6757623 0.3456848
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
ggplot(data = df, mapping = aes(x = total.sulfur.dioxide, y = quality)) +
geom_point()
ggplot(data = df, mapping = aes(x = residual.sugar, y = quality)) +
geom_point()
There is really no relationship. This is probably an exercise in clusterting or machine learning, but linear regression is insufficient.